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The CRIME Package

Version 1.4

Marcus Bishop
Email: marcus.bishop@gmail.com

Copyright

© 2006, 2007 Marcus Bishop

CRIME is free software which is distributed under the GNU Public Licence, version 2, and may be redistributed under the GNU Public Licence, version 2 or later (at your preference). See the file COPYING for detailed information

Acknowledgements

This project would not have been possible without Jon Carlson. Jon devised the algorithms used by ProjectiveResolution, CohomologyGenerators, and CohomologyRelators, having already implemented them in Magma, and shared these programs with me.

Contents

1 Introduction
 1.1 Installation and Loading
 1.2 For Further Information
2 Usage
 2.1 Cohomology Objects

  2.1-1 CohomologyObject
 2.2 Minimal Projective Resolutions

  2.2-1 ProjectiveResolution
  2.2-2 BoundaryMap
 2.3 Cohomology Generators and Relators

  2.3-1 CohomologyGenerators
  2.3-2 CohomologyRelators
 2.4 Tests for Completion
 2.5 Cohomology Rings

  2.5-1 CohomologyRing
  2.5-2 IsHomogeneous
  2.5-3 Degree
  2.5-4 LocateGeneratorsInCohomologyRing
 2.6 What Happens if n Isn't Big Enough?
 2.7 Induced Maps

  2.7-1 InducedHomomorphismOnCohomology
  2.7-2 SubgroupInclusion
 2.8 Massey Products

  2.8-1 MasseyProduct
A Some Benchmarks
B Leisure and Recreation: Cohomology Rings of all Groups of Size 16

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